Propositions REF  and REF  state the benchmarks
for the minimax optimal separation and localisation rates,
which have been established under the special case
where \(\lbrace \varepsilon _t\rbrace _{t = 1}^n\)  are i.i.d. (sub-)Gaussian random variables.
To the best of our knowledge, there do not exist equivalent results
on the detection lower bound or the localisation rate (when \(q_n \rightarrow \infty \) )
beyond the i.i.d. sub-Gaussianity.
For the AMOC alternative,
it is well known that the minimax optimal localisation rate is given by \(O_P(1)\) 
(see [1]}),
i.e. \(\rho _n \rightarrow \infty \)  arbitrarily slow in (REF ).
This rate extends beyond Gaussianity and independence
when there are a finite number of change points,
see Corollary 4.4 of [2]}.
